Question 39346: I asked this question before, but I did not get all the parts to the uestion posted for some reason. So please help. This includes all the parts, plus some of the answers if my answers are correct. Thanks a bunch.
1) Use the arithmetic sequence of numbers 2, 4, 6, 8, 10… to find the following:
a) What is d, the difference between any 2 terms?
Answer: d=4
Show work in this space. work below
The value of the 20th term, i.e., when n=20, is found by using the general term: for a=3, d=4, and n=20, its value is 3+(20−1)4=79
b) Using the formula for the nth term of an arithmetic sequence, what is 101st term? Answer:
Show work in this space.
B.sequences
To find the value of the nth term in an arithmetic sequence, use the following equation:
an = a1 + (n–1)d
a is the standard variable used to represent a term in a sequence and n counts the term number, so an represents the term in the sequence that you’re trying to find. d is the constant. To solve the problem, just substitute 101 for n, –3 for a1, and 5 for d.
a101 = -3 + (101 – 1)5
a101 = 497 part B
c) Using the formula for the sum of an arithmetic series, what is the sum of the first 20 terms?
Answer: The sum of the first 29 terms would be 79
Show work in this space.
work above.
d) Using the formula for the sum of an arithmetic series, what is the sum of the first 30 terms?
Answer:
Show work in this space.
e) What observation can you make about these sums of this series (HINT: It would be beneficial to find a few more sums like the sum of the first 2, then the first 3, etc.)?
Answer:
Answer by longjonsilver(2297)   (Show Source):
You can put this solution on YOUR website! sorry for sounding so harsh here, but reading some of your/somebody's answers, it is difficult to grasp what you have done or what you truly understand about this topic.
1. d is the common difference between terms in an arithmetic series/progression. In English, it is "the amount to add on to a term to make the next term" and so on and so on. So, given the series 2,4,6,8,10,... i cannot see how you make d equal to 4?
What do you add to 2 to make 4?
What do you add to 4 to make 6?
What do you add to 6 to make 8?
What do you add to 8 to make 10? etc
All of these say "2". So, d=2.
Right: if you could not "see" this, how would you work out d in this situation? Just get 2 adjacent terms, like 6, 8 and subtract: 8-6 is 2. Job done!
Beyond this point, you seem to be using different sequences of numbers. You mention a=3. This has nothing to do with the 2,4,6,8,10 sequence in part a. So i do not follow. Please be very clear in what you require for each part of your questions.
Please:
1. read my Lesson on arithmetic series (others have probably written some Lessons too).
2. try doing your questions yourself first after reading the lesson(s)
3. re-submit the questions (if you are still stuck) but make it clear what the sequence of numbers is for each part of the question. Currently it isn't clear and i guess that is why tutors are not answering this.
Hope this helps, somewhat :-)
Jon.
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